A lawyer representing Chris Gard and Connie Yates told the High Court "time had run out" for the baby.
Mr Gard said it meant his "sweet, gorgeous, innocent little boy" will not reach his first birthday on 4 August.
"To let our beautiful little Charlie go" is "the hardest thing we'll ever have to do", his mother said.
Charlie's parents said they made the decision because a US doctor had told them it was now too late to give Charlie nucleoside therapy.
"We only wanted to give him a chance of life," Ms Yates told the court in a statement.
